Dayanikli doğrusal olmayan regresyon yöntemleri

Regression analysis is a statistical method for modelling the relationship between two or more variables. Ordinary least squares regression, which is the most commonly used approach to determine relationship between variables may be misleading in the presence of outliers, or when there is heteroscedasticity and non-normality. Even if the underlying assumptions such as normality and homoscedasticity are hold, the relationship between dependent variable and independent variable(s) may be nonlinear. In such cases, using nonparametric regression methods is more appropriate since the shape of the regression function is not needed to be predefined and there is no significant assumptions as in parametric regression situation. The nonparametric regression estimators are called as smoothers and in this thesis four of them are investigated: Kernel smoothing, locally weighted scatter plot smoothing (LOWESS), the running interval smoother (RIS) and constrained b-spline smoothing (COBS). While the running interval smoother predicts the dependent variable by using different location estimators, COBS predicts by using quantiles and the other methods predict the dependent variable using weighted mean. Robust nonlinear regression methods are also blended to create alternative methods. The smoothers and these alternative methods are compared with a simulation study by using theoretical distributions. Furthermore, the methods are examined graphically to understand how the methods can model the relationship between variables. The predicted values of dependent variable corresponding to new observations are calculated as well. COBS and RIS with NO estimator outperformed the other methods in terms of mean squared error (MSE).